{"paper":{"title":"Implicit Linear Algebra and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"H. Narayanan","submitted_at":"2016-09-22T17:15:15Z","abstract_excerpt":"Linear systems often involve, as a basic building block, solutions of equations of the form \\begin{align*} A_Sx_S&+A_Px_P =0\\\\ A'_Sx_S & =0, \\end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither $x_S$ nor $x_P$ can be written as a function of the other but they are linked through the linear relationship, that of $(x_S,x_P) $ belonging to $\\mathcal{V}_{SP},$ the solution space of the first of the two equations. If $\\mathcal{V}_{S}$ is the solution space of the second equation, we may regard the final space of solutions $\\mathcal{V}_{P}$ as derived from "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07991","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}